Most fault locators are based on measurement of the reactance between a short circuit and that end of the transmission line where the fault locator is placed. The accuracy in the distance determination is, however, influenced by the fault resistance. The reason for this is that the current which flows through the fault resistance is somewhat offset in phase relative to the phase position of the current measured at the end of the transmission line, inter alia due to the current of the transmission line, before the occurrence of the fault. This means that the fault resistance is recognized as an apparent impedance with one resistive and one reactive component. It is this reactive component which gives rise to the inaccuracy of the fault in the distance determination since it influences the measured reactance.
A number of different ways of compensating for or reducing the influence of the phase difference during the fault distance determination have been described. Characteristic of most methods is that they try in some way to determine the fault current as accurately as possible. One method is described in an article in IEE Proc. Vol. 130, Pt. C, No. 6, November 1983, pp. 311-314, "Accurate fault impedance locating algorithm" by A. Wiszniewski. To sum up, this method means that the fault current is determined by summing up the phase currents, which means that the fault current is assumed to be equal to the unbalanced current in the ground conductor. Correction of the fault in the distance determination according to the article is further based on an estimation of the phase difference between the total current in the transmission line after the occurrence of a fault and the current through the fault resistance. The disadvantage of this method is that the unbalanced current is not always a good measure of the current flowing at the fault point owing to the fact that the fault current distribution for the zero-sequence current, that is, the distribution factor D.sub.AO is less reliable than the distribution factor for the positive-sequence current D.sub.A. In addition, a large part of the zero-sequence current can often be shunted away in transformers connected to the object to be protected.
Another method is described in an article "An accurate fault locator with compensation for apparent reactance in the fault resistance resulting from remote-end infeed", published in IEEE Transaction on PAS, Vol. PAS-104, No. 2, Feb. 1984, pp 424-436. Besides taking into consideration the impedance Z.sub.1 of the transmission line, this fault locator also takes into consideration the source impedances of the transmission line to be able correctly to describe the network and the influence of the supply to the fault current of current from both directions with the aid of the distribution factor D.sub.A. According to this method, sampled phase currents, measured at a measuring station A at one end of the line, are memorized to be able to determine the change in the currents at the measuring station which arises when a fault occurs, that is, the current change I.sub.FA equal to the actual load and fault current I.sub.A minus the load current before the occurrence of the fault. The voltage U.sub.A at the measuring station A can thereby be expressed as the sum of the voltage drop I.sub.A .multidot.p.multidot.Z.sub.l across that part of the line which is located between the measuring station and the fault point plus the fault voltage I.sub.F .multidot.R.sub.F where I.sub.F is the current which flows through the fault resistance R.sub.F, that is, EQU U.sub.A =I.sub.A .multidot.p.multidot.Z.sub.l +I.sub.F .multidot.R.sub.F ( 1)
where "p" is the relative distance to the fault.
Because the current I.sub.F which flows through the fault resistance has a current contribution also from a supply station at the other end of the transmission line, I.sub.F will be different from I.sub.FA. The relationship between these is determined by the above-mentioned distribution factor as follows EQU I.sub.FA =D.sub.A .multidot.I.sub.F ( 2)
Further, without going into detail, it can be demonstrated that EQU I.sub.FA =3/2(.DELTA.I.sub.A -I.sub.0A) (3)
where .DELTA.I.sub.A is the sum of changes in the symmetrical current components measured at A and I.sub.0A is the zero-sequence component which occurs in the even of a fault. In addition, since EQU .DELTA.I.sub.A -I.sub.0A =.DELTA.I.sub.1A +.DELTA.I.sub.2A ( 4)
this means that the current change--measured at A--which occurs upon a fault can be expressed with the aid of the sum of changes in the positive- and negative-sequence currents at the measuring point A. With knowledge of the value of these currents, I.sub.FA can be determined, and since also D.sub.A is known for the network in question, I.sub.F can be determined as follows EQU I.sub.F =I.sub.FA /D.sub.A =3/2(.DELTA.I.sub.1A +.DELTA.I.sub.2A)/D.sub.A ( 5)
This is normally expressed in such a way that as fault current there is used the zero-sequence-free part of the current change which occurs in the event of a fault. The method for solution means that equation (1) can now be written as EQU U.sub.A =I.sub.A .multidot.p.multidot.Z.sub.l +(I.sub.FA /D.sub.A).multidot.R.sub.F ( 1a)
which leads to a quadratic equation for solution of "p".
The reason for using as a measure of the fault current the zero-sequence-free part of the current changes is that the zero-sequence impedances of the network have a lower angle and are less reliable than the positive-sequence impedances. The corresponding distribution factor thus becomes less reliable and hence also the phase angle between actual and measured fault currents becomes less reliable.
The described method of obtaining the fault current, however, is no method that can be used when high demands are placed on fast protective functions. The reasons for this are, inter alia, that currents both before and after a fault has occurred are Fourier filtered to obtain the fundamental components of the currents and that the method of calculation for solving "p" is relatively extensive.
Another way of obtaining a measure of the fault current is described in an article entitled "Microprocessor-implemented digital filters for the calculation of symmetrical components" by A. J. Degens, published in IEE Proc., Vol. 129, Pt. C, No. 3, pp. 111-118, May 1982. However, this method for determining the fault current requires that the sampling frequency is a multiple of the network frequency and that a number of older samples are memorized. This means that a considerable amount of time passes before the filter for obtaining the fault current has become adapted to the new conditions after a fault has occurred on the power network.